Talks are fluid, as are the possible pairings, the people said. The scenario is among a few that Blackstone is working on in which the private-equity giant could team up with a partner to buy all or part of the computer maker, the people said.

Any of those deals would be a rival to Dell’s agreement to sell the company to founder and Chief Executive Michael Dell and private-equity firm Silver Lake Partners for $24.4 billion. As part of a “go shop” process that ends Friday, the company is now seeking counterbids.

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Deal Journal is an up-to-the-minute take on the deals and deal makers that shape the landscape of Wall Street, including mergers and acquisitions, capital-raising, private equity and bankruptcy. In short, wherever money changes hands. Deal Journal is updated throughout each trading day with exclusive commentary, analysis, data, news flashes and profiles. The Wall Street Journal’s David Benoit is the lead writer, with contributions from other Journal reporters and editors. Send news items, comments and questions to deals@wsj.com.